Contemporary Mathematics can not reach agreement on its principles, axioms and conclusions of true knowledge and perspectives of development. And it doesn’t notice that the same issues were considered by Plato, who found an an-swer in his «Dialogues». The proposed hierarchy of generalizations allows us to understand the algorithm of induction invented by Plato, ideal numbers built by him, their mathematics and the use of all this to find the truth of any thoughts. Inductive-deductive method of Plato becomes an alternative to the axiomatic method, simplifies the training and use of mathematics, constructed by the algorithm of induction without the axioms up to the Universal Mind.Keywords: Mathematics, induction, algorithm, Plato.